Dynamic imaging is commonly used in magnetic resonance imaging (MRI), and MRI acceleration techniques can provide enhanced spatial resolution, temporal resolution, and/or spatial coverage for these applications. Compressed sensing (CS), an acceleration technique of growing importance, is making a major impact on MRI (1). Using CS, high-quality images can be recovered from data sampled well below the Nyquist rate, provided that the sampling pattern is incoherent, the images are sparse in a transform domain, and a sparsity-promoting iterative reconstruction is used (1). Because of the high temporal and spatial redundancy inherent to dynamic contrast-enhanced MRI, these data can be represented sparsely in a transform domain and are suited for acceleration by CS (2). However, patient motion due to respiratory or other factors reduces the spatiotemporal redundancy of the data and, if not corrected, leads to image artifacts (3-11). The problem of imperfect breathholding and associated respiratory motion, for example, presents a major challenge to CS-acceleration of first-pass cardiac MRI where, even when patients are instructed to suspend respiration for 15-20 seconds, they are often unable to comply fully with instructions and they breathe during the scan.
A number of CS methods have been developed to accelerate dynamic MRI. Early studies such as k-t SPARSE showed that sparsity in the spatial and temporal frequency (x-f) domain could be exploited to accelerate cine MRI using CS (12,13). The k-t FOCal Underdetermined System Solver (k-t FOCUSS) method made improvements to x-f domain approaches by separating the data into predicted and residual signals, where the predicted signal served as a baseline signal and sparsity was exploited for the residual signal (4). While x-f domain methods combined with parallel imaging have been successfully used for dynamic contrast-enhanced MRI (3), the non-periodic nature of dynamic contrast-enhanced MRI leads to a broader band of temporal frequencies than cine MRI, thus these applications present less x-f sparsity than cine MRI. For these cases, data-driven spatiotemporal basis functions such as those used in Partially Separable Functions (14) and the k-t Sparsity and Low-Rank (k-t SLR) method (6) may have advantages. For example, the k-t SLR method, which is applied in the image-time domain and exploits matrix rank sparsity by decomposing the signal using singular value decomposition (SVD), has provided good image quality for accelerated contrast-enhanced cardiac perfusion imaging (6). However, even while advanced sparsifying transforms such as SVD provide improved image quality, these approaches are still subject to artifacts when respiratory motion or other patient movement occurs.
One approach to handle complex dynamics such as breathing is to extract motion information from the acquired data and apply motion compensation during CS reconstruction. Some studies (7,15) base their work on Batchelor's motion matrix method (16) to correct for respiratory motion in free-breathing or real-time cine imaging. While this approach separates cardiac and respiratory motion, the data binning step limits its extension to wider applications such as dynamic perfusion imaging and relaxation imaging. Another approach is to compensate the image dataset for motion and then apply a CS sparsity transform to the motion-compensated data, such as in k-t FOCUSS with motion estimation and compensation (4) and the recent method of Motion-Adaptive Spatio-Temporal Regularization (MASTeR) (17), as well as other methods (3,10,18). To date, these methods have employed the temporal difference or x-f methods as the sparsifying transform, and the results demonstrate advantages afforded by motion compensation.
It is with respect to these and other considerations that the various embodiments described below are presented.